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LIMIT STATE DESIGN
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What is Limit State?
A l imit state is a state of impending failure, beyondwhich a structure ceases to perform its intended
function satisfactorily, in terms of either safety or
serviceability.
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DESIGN CONCEPTS
Safety:implies that the likelihood of (partial or total) col lapse of
structure is acceptably low not only under (normal infected loads)
service loads but also under overloads.
Serviceability:satisfactory performance of structure under serviceloads without discomfort to user due to excessive deflections,
cracking, vibration etc.
Other considerations such asdurabil i ty, impermeabil ity, acoustic
and thermal insulation etc.
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Limit State DesignL imit States
Purpose: to achieve acceptable probabil i ty that a structure wil l not
become unfit for its intended use i.e. that it wil l not reach a l imit
state.
Thus, a structure ceases to be fit for use will consti tute a limit state
and the design aims to avoid any such condi tion being reached
dur ing the expected li fe of the structure.
Two principle types of l imit state are;
i . U ltimate Limi t State
ii. Serviceability L imit State
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Limit State Design
Ul timate L imit State
This requi res that the structure must be able to withstand, with an
adequate factor of safety against collapse, the loads for which it is
designed.
Limit state of Collapse: flexure, shear, compression, torsion,
bearing, etc.
Possibility of buckling or overturning must also be taken into
account, as must the possibil i ty of accidental damage as caused, for
example, by an internal explosion.
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Serviceability Limit States
Most important serviceabil i ty limit states are
Deflection: appearance or eff iciency of any part of the structure
must not be adversely affected by deflections.
Cracking: local damage due to cracking and spall ing must not
affect the appearance, eff iciency or durabil i ty of structure.
Durabil i ty: this must be considered in terms of the proposed li fe
of the structure and its conditions of exposure.
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Serviceability Limit States
Other l imit states include
Excessive vibration: which may cause discomfort or alarm as well
as damage.
Fatigue: must be considered if cyclic loading is l ikely.
F ire resistance: this must be considered in terms of resistance to
collapse, flame penetration and heat transfer.
Special cir cumstances: any special requirements of the structure
which are not covered by any of the more common limit states,
such as earthquake resistance, must be taken into account.
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Assumptions for Design in Flexure
1. At any cross-section, sections which are plane prior to
bending remain plane after bending. Or strain varies
linearly with distance from neutral axis i.e. plane
sections remain plane in bending.
2. The maximum strain in concrete at the outermost fiber
is 0.0035.
3. Stress-strain relationship in concrete could be either
rectangular, parabolic or combination of rectangular
and parabolic curves which should be agreeable with
the exper imental results.
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Assumptions for Design in Flexure
4. The stresses in steel bars used for reinforcement are
derived from the representative stress-strain curve forthe type of steel used.
5. Perfect bond between reinforced steel and adjoining
concrete.
6. Tensi le strength of concrete is neglected.
7. M inimum strain in steel reinforcement should not be
less than ((0.87fy/Es) + 0.002).
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What is partial safety factor?
I n L imit State Design, the load actually used for each
limit state is called theDesign Load for that limit
state
Design Load is the product of the character istic load
and the relevant partial safety factor for loads
Design load = fx (character istic load)
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Partial safety factor is intended to cover those variations
in loading in design or in construction which are likely
to occur after the designer and the constructor have
each exercised careful ly their ski l l and knowledge.
Also takes into account nature of limit state in question.
Why do we use partial safety factors?
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Partial Factors of Safety
Other possible variations such as constructional
tolerances are allowed for by partial factors of safety
applied to the strength of materials and to loadings.
Lack of adequate data, however, makes thisunrealistic and in practice the values adopted are
based on experience and simplified calculations.
i f f f f ( )
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Partial factors of safety for loads (f)
Errors and inaccuracies may be due to a number of causes:
Design assumptions and inaccuracy of calculation.
Possible unusual load increases.
Unforeseen stress redistr ibutions.
Constructional inaccuracies
These are taken into account by applying a particular factor of
safety(f) on the loadings, so that
Design load = character istic load x partial factor of safety(f)
This factor should also take into account the importance of the
limit state under consideration and ref lect to some extent the
accuracy with which different type of loading can be predicted,
and the probabil i ty of particular load combinations occurr ing.
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Partial Factor of Safety for loads
LoadCombination
Limit State of Collapse Limit State of Serviceability
DL LL WL/EL DL LL WL/EL
DL + LL 1.5 1.5 1.0 1.0 1.0 --
DL + WL or EL1.5 or
0.9*- 1.5 1.0 --- 1.0
DL + LL + WL/EL 1.2 1.2 1.2 1.0 0.8 0.8
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What is Design Strength?
I n design calculationsDesignStrength for a givenmaterial and limit state is obtained by dividing the
character istic strength by the partial safety factor for
strength, appropriate to that material and that limitstate.
When assessing the strength of a structure or structural
member for the limit state of collapse, the partial safety
factor should be taken as 1.5 for concrete and 1.15 for
steel
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Partial Factors of Safety for Materials(m)
The strength of mater ial in an actual member wil l dif fer
from that measured in a carefully prepared test specimen
and it is particularly true for concrete where placing,
compaction and cur ing are so important to the strength.
Steel, on the other hand, is a relatively consistent mater ial
requir ing a small partial factor of safety.
The sever ity of the limit state being considered. Thus, higher
values are taken for the ul timate l imit state than for the
serviceabi l i ty limit state.
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0.002 0.0035Strain
fck
0.67 fck
0.67 fck/mStress
Parabolic
Curve
Stress-Strain Curve for Concrete in Flexural Compression
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Strain diagram and Stress blocks:(a) Section; (b) Strain diagram; (c) Stress block
d
b
Ast
xu
0.0035
cu
s
0.446 fck
xu
0.87 fy
(a) (b)
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0.42 xu
0.36 fckxuxu
Stress Block Parameters
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